Details

Time bar (total: 38.8s)

sample130.0ms

Algorithm
intervals
Results
114.0ms621×body80valid

simplify169.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
169.0ms
(- (+ (pow (+ (* a a) (* b b)) 2) (* 4 (+ (* (* a a) (+ 1 a)) (* (* b b) (- 1 (* 3 a)))))) 1)

prune23.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize29.0ms

Local error

Found 4 expressions with local error:

0.2b
(fma (fma b b (* a a)) (fma b b (* a a)) -1)
0.0b
(fma (* a a) a (* a a))
0.0b
(fma -3 a 1)
0.0b
(fma (fma (* b b) (fma -3 a 1) (fma (* a a) a (* a a))) 4 (fma (fma b b (* a a)) (fma b b (* a a)) -1))

rewrite2.0ms

Algorithm
rewrite-expression-head
Rules
4×add-sqr-sqrt expm1-log1p-u pow1 *-un-lft-identity add-cbrt-cube add-exp-log add-cube-cbrt fma-udef insert-posit16 log1p-expm1-u add-log-exp
Counts
4 → 44
Calls
4 calls:
Slowest
0.0ms
(fma (fma b b (* a a)) (fma b b (* a a)) -1)
0.0ms
(fma (fma (* b b) (fma -3 a 1) (fma (* a a) a (* a a))) 4 (fma (fma b b (* a a)) (fma b b (* a a)) -1))
0.0ms
(fma (* a a) a (* a a))
0.0ms
(fma -3 a 1)

series409.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
136.0ms
(fma (fma (* b b) (fma -3 a 1) (fma (* a a) a (* a a))) 4 (fma (fma b b (* a a)) (fma b b (* a a)) -1))
128.0ms
(fma (* a a) a (* a a))
110.0ms
(fma (fma b b (* a a)) (fma b b (* a a)) -1)
34.0ms
(fma -3 a 1)

simplify1.6s

Counts
12 → 56
Calls
12 calls:
Slowest
316.0ms
(+ (pow b 4) (+ (* 2 (* (pow a 2) (pow b 2))) (pow a 4)))
311.0ms
(+ (pow b 4) (+ (* 2 (* (pow a 2) (pow b 2))) (pow a 4)))
289.0ms
(+ (pow b 4) (+ (* 2 (* (pow a 2) (pow b 2))) (pow a 4)))
277.0ms
(+ (pow b 4) (+ (* 2 (* (pow a 2) (pow b 2))) (pow a 4)))
174.0ms
(- (+ (* 4 (pow a 2)) (* 4 (pow b 2))) 1)

prune858.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.1b

localize70.0ms

Local error

Found 4 expressions with local error:

0.2b
(cbrt (fma (fma b b (* a a)) (fma b b (* a a)) -1))
0.2b
(cbrt (fma (fma b b (* a a)) (fma b b (* a a)) -1))
0.2b
(cbrt (fma (fma b b (* a a)) (fma b b (* a a)) -1))
0.2b
(* (cbrt (fma (fma b b (* a a)) (fma b b (* a a)) -1)) (cbrt (fma (fma b b (* a a)) (fma b b (* a a)) -1)))

rewrite13.0ms

Algorithm
rewrite-expression-head
Rules
25×cbrt-prod
23×add-sqr-sqrt
15×*-un-lft-identity add-cube-cbrt
11×pow1
9×pow1/3
6×swap-sqr associate-*r* associate-*l* add-exp-log
4×expm1-log1p-u add-cbrt-cube insert-posit16 log1p-expm1-u add-log-exp unswap-sqr
2×pow-prod-down pow-sqr pow-prod-up
1×pow2 pow-plus prod-exp *-commutative cbrt-unprod
Counts
4 → 85
Calls
4 calls:
Slowest
9.0ms
(* (cbrt (fma (fma b b (* a a)) (fma b b (* a a)) -1)) (cbrt (fma (fma b b (* a a)) (fma b b (* a a)) -1)))
1.0ms
(cbrt (fma (fma b b (* a a)) (fma b b (* a a)) -1))
1.0ms
(cbrt (fma (fma b b (* a a)) (fma b b (* a a)) -1))
1.0ms
(cbrt (fma (fma b b (* a a)) (fma b b (* a a)) -1))

series886.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
245.0ms
(* (cbrt (fma (fma b b (* a a)) (fma b b (* a a)) -1)) (cbrt (fma (fma b b (* a a)) (fma b b (* a a)) -1)))
244.0ms
(cbrt (fma (fma b b (* a a)) (fma b b (* a a)) -1))
224.0ms
(cbrt (fma (fma b b (* a a)) (fma b b (* a a)) -1))
173.0ms
(cbrt (fma (fma b b (* a a)) (fma b b (* a a)) -1))

simplify11.2s

Counts
65 → 97
Calls
65 calls:
Slowest
356.0ms
(* (cbrt (sqrt (fma (fma b b (* a a)) (fma b b (* a a)) -1))) (sqrt (cbrt (fma (fma b b (* a a)) (fma b b (* a a)) -1))))
349.0ms
(+ (log (cbrt (fma (fma b b (* a a)) (fma b b (* a a)) -1))) (log (cbrt (fma (fma b b (* a a)) (fma b b (* a a)) -1))))
313.0ms
(cbrt (fma (fma b b (* a a)) (fma b b (* a a)) -1))
310.0ms
(* (cbrt (cbrt (fma (fma b b (* a a)) (fma b b (* a a)) -1))) (cbrt (cbrt (fma (fma b b (* a a)) (fma b b (* a a)) -1))))
300.0ms
(cbrt (sqrt (fma (fma b b (* a a)) (fma b b (* a a)) -1)))

prune1.3s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize50.0ms

Local error

Found 4 expressions with local error:

0.2b
(cbrt (* (* (cbrt (fma (fma b b (* a a)) (fma b b (* a a)) -1)) (cbrt (fma (fma b b (* a a)) (fma b b (* a a)) -1))) (cbrt (fma (fma b b (* a a)) (fma b b (* a a)) -1))))
0.2b
(cbrt (fma (fma b b (* a a)) (fma b b (* a a)) -1))
0.2b
(cbrt (fma (fma b b (* a a)) (fma b b (* a a)) -1))
0.2b
(cbrt (fma (fma b b (* a a)) (fma b b (* a a)) -1))

rewrite24.0ms

Algorithm
rewrite-expression-head
Rules
10×cbrt-prod
7×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
4×expm1-log1p-u pow1 add-cbrt-cube pow1/3 add-exp-log insert-posit16 log1p-expm1-u add-log-exp
1×pow3 rem-cbrt-cube
Counts
4 → 55
Calls
4 calls:
Slowest
22.0ms
(cbrt (* (* (cbrt (fma (fma b b (* a a)) (fma b b (* a a)) -1)) (cbrt (fma (fma b b (* a a)) (fma b b (* a a)) -1))) (cbrt (fma (fma b b (* a a)) (fma b b (* a a)) -1))))
1.0ms
(cbrt (fma (fma b b (* a a)) (fma b b (* a a)) -1))
1.0ms
(cbrt (fma (fma b b (* a a)) (fma b b (* a a)) -1))
1.0ms
(cbrt (fma (fma b b (* a a)) (fma b b (* a a)) -1))

series679.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
176.0ms
(cbrt (fma (fma b b (* a a)) (fma b b (* a a)) -1))
174.0ms
(cbrt (* (* (cbrt (fma (fma b b (* a a)) (fma b b (* a a)) -1)) (cbrt (fma (fma b b (* a a)) (fma b b (* a a)) -1))) (cbrt (fma (fma b b (* a a)) (fma b b (* a a)) -1))))
166.0ms
(cbrt (fma (fma b b (* a a)) (fma b b (* a a)) -1))
163.0ms
(cbrt (fma (fma b b (* a a)) (fma b b (* a a)) -1))

simplify1.7s

Counts
23 → 67
Calls
23 calls:
Slowest
239.0ms
(cbrt (* (cbrt (fma (fma b b (* a a)) (fma b b (* a a)) -1)) (cbrt (fma (fma b b (* a a)) (fma b b (* a a)) -1))))
226.0ms
(cbrt (sqrt (fma (fma b b (* a a)) (fma b b (* a a)) -1)))
226.0ms
(cbrt (sqrt (fma (fma b b (* a a)) (fma b b (* a a)) -1)))
213.0ms
(cbrt (* (cbrt (fma (fma b b (* a a)) (fma b b (* a a)) -1)) (cbrt (fma (fma b b (* a a)) (fma b b (* a a)) -1))))
211.0ms
(cbrt (* (cbrt (fma (fma b b (* a a)) (fma b b (* a a)) -1)) (cbrt (fma (fma b b (* a a)) (fma b b (* a a)) -1))))

prune1.0s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.0b

localize50.0ms

Local error

Found 4 expressions with local error:

0.2b
(cbrt (fma (fma (* b b) (fma -3 a 1) (fma (* a a) a (* a a))) 4 (fma (fma b b (* a a)) (fma b b (* a a)) -1)))
0.2b
(cbrt (fma (fma (* b b) (fma -3 a 1) (fma (* a a) a (* a a))) 4 (fma (fma b b (* a a)) (fma b b (* a a)) -1)))
0.2b
(cbrt (fma (fma (* b b) (fma -3 a 1) (fma (* a a) a (* a a))) 4 (fma (fma b b (* a a)) (fma b b (* a a)) -1)))
0.2b
(* (cbrt (fma (fma (* b b) (fma -3 a 1) (fma (* a a) a (* a a))) 4 (fma (fma b b (* a a)) (fma b b (* a a)) -1))) (cbrt (fma (fma (* b b) (fma -3 a 1) (fma (* a a) a (* a a))) 4 (fma (fma b b (* a a)) (fma b b (* a a)) -1))))

rewrite22.0ms

Algorithm
rewrite-expression-head
Rules
25×cbrt-prod
23×add-sqr-sqrt
15×*-un-lft-identity add-cube-cbrt
11×pow1
9×pow1/3
6×swap-sqr associate-*r* associate-*l* add-exp-log
4×expm1-log1p-u add-cbrt-cube insert-posit16 log1p-expm1-u add-log-exp unswap-sqr
2×pow-prod-down pow-sqr pow-prod-up
1×pow2 pow-plus prod-exp *-commutative cbrt-unprod
Counts
4 → 85
Calls
4 calls:
Slowest
19.0ms
(* (cbrt (fma (fma (* b b) (fma -3 a 1) (fma (* a a) a (* a a))) 4 (fma (fma b b (* a a)) (fma b b (* a a)) -1))) (cbrt (fma (fma (* b b) (fma -3 a 1) (fma (* a a) a (* a a))) 4 (fma (fma b b (* a a)) (fma b b (* a a)) -1))))
1.0ms
(cbrt (fma (fma (* b b) (fma -3 a 1) (fma (* a a) a (* a a))) 4 (fma (fma b b (* a a)) (fma b b (* a a)) -1)))
1.0ms
(cbrt (fma (fma (* b b) (fma -3 a 1) (fma (* a a) a (* a a))) 4 (fma (fma b b (* a a)) (fma b b (* a a)) -1)))
1.0ms
(cbrt (fma (fma (* b b) (fma -3 a 1) (fma (* a a) a (* a a))) 4 (fma (fma b b (* a a)) (fma b b (* a a)) -1)))

series1.0s

Counts
4 → 12
Calls
4 calls:
Slowest
297.0ms
(* (cbrt (fma (fma (* b b) (fma -3 a 1) (fma (* a a) a (* a a))) 4 (fma (fma b b (* a a)) (fma b b (* a a)) -1))) (cbrt (fma (fma (* b b) (fma -3 a 1) (fma (* a a) a (* a a))) 4 (fma (fma b b (* a a)) (fma b b (* a a)) -1))))
266.0ms
(cbrt (fma (fma (* b b) (fma -3 a 1) (fma (* a a) a (* a a))) 4 (fma (fma b b (* a a)) (fma b b (* a a)) -1)))
236.0ms
(cbrt (fma (fma (* b b) (fma -3 a 1) (fma (* a a) a (* a a))) 4 (fma (fma b b (* a a)) (fma b b (* a a)) -1)))
235.0ms
(cbrt (fma (fma (* b b) (fma -3 a 1) (fma (* a a) a (* a a))) 4 (fma (fma b b (* a a)) (fma b b (* a a)) -1)))

simplify11.3s

Counts
65 → 97
Calls
65 calls:
Slowest
531.0ms
(* (sqrt (cbrt (fma (fma (* b b) (fma -3 a 1) (fma (* a a) a (* a a))) 4 (fma (fma b b (* a a)) (fma b b (* a a)) -1)))) (sqrt (cbrt (fma (fma (* b b) (fma -3 a 1) (fma (* a a) a (* a a))) 4 (fma (fma b b (* a a)) (fma b b (* a a)) -1)))))
438.0ms
(- (pow -1 1/3) (+ (* 4/3 (* (pow b 2) (pow -1 1/3))) (* 4/3 (* (pow a 2) (pow -1 1/3)))))
404.0ms
(- (pow -1 1/3) (+ (* 4/3 (* (pow b 2) (pow -1 1/3))) (* 4/3 (* (pow a 2) (pow -1 1/3)))))
366.0ms
(* (fma (fma (* b b) (fma -3 a 1) (fma (* a a) a (* a a))) 4 (fma (fma b b (* a a)) (fma b b (* a a)) -1)) (fma (fma (* b b) (fma -3 a 1) (fma (* a a) a (* a a))) 4 (fma (fma b b (* a a)) (fma b b (* a a)) -1)))
360.0ms
(- (pow -1 1/3) (+ (* 4/3 (* (pow b 2) (pow -1 1/3))) (* 4/3 (* (pow a 2) (pow -1 1/3)))))

prune1.2s

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 0.0b

regimes192.0ms

Accuracy

0% (0.1b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 0.2b

bsearch2.0ms

end0.0ms

sample4.7s

Algorithm
intervals
Results
3.9s20442×body80valid