Details

Time bar (total: 45.0s)

sample90.0ms

Algorithm
intervals
Results
69.0ms626×body80valid

simplify215.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
215.0ms
(- (+ (pow (+ (* a a) (* b b)) 2) (* 4 (* b b))) 1)

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize13.0ms

Local error

Found 1 expressions with local error:

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

rewrite1.0ms

Algorithm
rewrite-expression-head
Rules
1×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
1 → 11
Calls
1 calls:
Slowest
0.0ms
(fma (fma a a (* b b)) (fma a a (* b b)) (fma (* b b) 4 -1))

series121.0ms

Counts
1 → 3
Calls
1 calls:
Slowest
121.0ms
(fma (fma a a (* b b)) (fma a a (* b b)) (fma (* b b) 4 -1))

simplify813.0ms

Counts
3 → 14
Calls
3 calls:
Slowest
357.0ms
(+ (pow b 4) (+ (pow a 4) (* 2 (* (pow a 2) (pow b 2)))))
295.0ms
(+ (pow b 4) (+ (pow a 4) (* 2 (* (pow a 2) (pow b 2)))))
160.0ms
(- (+ (pow a 4) (* 4 (pow b 2))) 1)

prune132.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.2b

localize31.0ms

Local error

Found 4 expressions with local error:

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

rewrite21.0ms

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
15.0ms
(* (cbrt (fma (fma a a (* b b)) (fma a a (* b b)) (fma (* b b) 4 -1))) (cbrt (fma (fma a a (* b b)) (fma a a (* b b)) (fma (* b b) 4 -1))))
1.0ms
(cbrt (fma (fma a a (* b b)) (fma a a (* b b)) (fma (* b b) 4 -1)))
1.0ms
(cbrt (fma (fma a a (* b b)) (fma a a (* b b)) (fma (* b b) 4 -1)))
1.0ms
(cbrt (fma (fma a a (* b b)) (fma a a (* b b)) (fma (* b b) 4 -1)))

series1.1s

Counts
4 → 12
Calls
4 calls:
Slowest
321.0ms
(* (cbrt (fma (fma a a (* b b)) (fma a a (* b b)) (fma (* b b) 4 -1))) (cbrt (fma (fma a a (* b b)) (fma a a (* b b)) (fma (* b b) 4 -1))))
264.0ms
(cbrt (fma (fma a a (* b b)) (fma a a (* b b)) (fma (* b b) 4 -1)))
248.0ms
(cbrt (fma (fma a a (* b b)) (fma a a (* b b)) (fma (* b b) 4 -1)))
247.0ms
(cbrt (fma (fma a a (* b b)) (fma a a (* b b)) (fma (* b b) 4 -1)))

simplify14.3s

Counts
65 → 97
Calls
65 calls:
Slowest
670.0ms
(- 1 (+ (* 2/3 (pow a 4)) (* 8/3 (pow b 2))))
485.0ms
(- (pow -1 1/3) (+ (* 1/3 (* (pow a 4) (pow -1 1/3))) (* 4/3 (* (pow b 2) (pow -1 1/3)))))
455.0ms
(- (pow -1 1/3) (+ (* 1/3 (* (pow a 4) (pow -1 1/3))) (* 4/3 (* (pow b 2) (pow -1 1/3)))))
412.0ms
(- (pow -1 1/3) (+ (* 1/3 (* (pow a 4) (pow -1 1/3))) (* 4/3 (* (pow b 2) (pow -1 1/3)))))
365.0ms
(* (cbrt (* (cbrt (fma (fma a a (* b b)) (fma a a (* b b)) (fma (* b b) 4 -1))) (cbrt (fma (fma a a (* b b)) (fma a a (* b b)) (fma (* b b) 4 -1))))) (cbrt (* (cbrt (fma (fma a a (* b b)) (fma a a (* b b)) (fma (* b b) 4 -1))) (cbrt (fma (fma a a (* b b)) (fma a a (* b b)) (fma (* b b) 4 -1))))))

prune1.2s

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 0.1b

localize23.0ms

Local error

Found 4 expressions with local error:

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

rewrite17.0ms

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
10.0ms
(* (cbrt (fma (fma a a (* b b)) (fma a a (* b b)) (fma (* b b) 4 -1))) (cbrt (fma (fma a a (* b b)) (fma a a (* b b)) (fma (* b b) 4 -1))))
4.0ms
(cbrt (fma (fma a a (* b b)) (fma a a (* b b)) (fma (* b b) 4 -1)))
1.0ms
(cbrt (fma (fma a a (* b b)) (fma a a (* b b)) (fma (* b b) 4 -1)))
1.0ms
(cbrt (fma (fma a a (* b b)) (fma a a (* b b)) (fma (* b b) 4 -1)))

series1.1s

Counts
4 → 12
Calls
4 calls:
Slowest
323.0ms
(* (cbrt (fma (fma a a (* b b)) (fma a a (* b b)) (fma (* b b) 4 -1))) (cbrt (fma (fma a a (* b b)) (fma a a (* b b)) (fma (* b b) 4 -1))))
274.0ms
(cbrt (fma (fma a a (* b b)) (fma a a (* b b)) (fma (* b b) 4 -1)))
262.0ms
(cbrt (fma (fma a a (* b b)) (fma a a (* b b)) (fma (* b b) 4 -1)))
252.0ms
(cbrt (fma (fma a a (* b b)) (fma a a (* b b)) (fma (* b b) 4 -1)))

simplify14.0s

Counts
65 → 97
Calls
65 calls:
Slowest
469.0ms
(- (pow -1 1/3) (+ (* 1/3 (* (pow a 4) (pow -1 1/3))) (* 4/3 (* (pow b 2) (pow -1 1/3)))))
433.0ms
(- (pow -1 1/3) (+ (* 1/3 (* (pow a 4) (pow -1 1/3))) (* 4/3 (* (pow b 2) (pow -1 1/3)))))
404.0ms
(- (pow -1 1/3) (+ (* 1/3 (* (pow a 4) (pow -1 1/3))) (* 4/3 (* (pow b 2) (pow -1 1/3)))))
349.0ms
(* (cbrt (fma (fma a a (* b b)) (fma a a (* b b)) (fma (* b b) 4 -1))) (cbrt (fma (fma a a (* b b)) (fma a a (* b b)) (fma (* b b) 4 -1))))
343.0ms
(* (sqrt (cbrt (fma (fma a a (* b b)) (fma a a (* b b)) (fma (* b b) 4 -1)))) (sqrt (cbrt (fma (fma a a (* b b)) (fma a a (* b b)) (fma (* b b) 4 -1)))))

prune1.4s

Pruning

15 alts after pruning (13 fresh and 2 done)

Merged error: 0.1b

localize38.0ms

Local error

Found 4 expressions with local error:

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

rewrite6.0ms

Algorithm
rewrite-expression-head
Rules
12×cbrt-prod
8×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
Counts
4 → 56
Calls
4 calls:
Slowest
1.0ms
(cbrt (fma (fma a a (* b b)) (fma a a (* b b)) (fma (* b b) 4 -1)))
1.0ms
(cbrt (fma (fma a a (* b b)) (fma a a (* b b)) (fma (* b b) 4 -1)))
1.0ms
(cbrt (fma (fma a a (* b b)) (fma a a (* b b)) (fma (* b b) 4 -1)))
1.0ms
(cbrt (fma (fma a a (* b b)) (fma a a (* b b)) (fma (* b b) 4 -1)))

series996.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
287.0ms
(cbrt (fma (fma a a (* b b)) (fma a a (* b b)) (fma (* b b) 4 -1)))
241.0ms
(cbrt (fma (fma a a (* b b)) (fma a a (* b b)) (fma (* b b) 4 -1)))
234.0ms
(cbrt (fma (fma a a (* b b)) (fma a a (* b b)) (fma (* b b) 4 -1)))
233.0ms
(cbrt (fma (fma a a (* b b)) (fma a a (* b b)) (fma (* b b) 4 -1)))

simplify4.3s

Counts
24 → 68
Calls
24 calls:
Slowest
510.0ms
(- (pow -1 1/3) (+ (* 1/3 (* (pow a 4) (pow -1 1/3))) (* 4/3 (* (pow b 2) (pow -1 1/3)))))
457.0ms
(- (pow -1 1/3) (+ (* 1/3 (* (pow a 4) (pow -1 1/3))) (* 4/3 (* (pow b 2) (pow -1 1/3)))))
445.0ms
(- (pow -1 1/3) (+ (* 1/3 (* (pow a 4) (pow -1 1/3))) (* 4/3 (* (pow b 2) (pow -1 1/3)))))
424.0ms
(- (pow -1 1/3) (+ (* 1/3 (* (pow a 4) (pow -1 1/3))) (* 4/3 (* (pow b 2) (pow -1 1/3)))))
331.0ms
(cbrt (* (cbrt (fma (fma a a (* b b)) (fma a a (* b b)) (fma (* b b) 4 -1))) (cbrt (fma (fma a a (* b b)) (fma a a (* b b)) (fma (* b b) 4 -1)))))

prune1.1s

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 0.0b

regimes362.0ms

Accuracy

0% (0.1b remaining)

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

bsearch1.0ms

end0.0ms

sample3.6s

Algorithm
intervals
Results
3.1s20385×body80valid