Details

Time bar (total: 58.2s)

sample64.0ms

Algorithm
intervals
Results
19.0ms245×body80valid
4.0ms14×body640valid
4.0ms11×body1280valid
4.0ms16×body320valid
1.0ms8×body160valid

simplify7.6s

Counts
1 → 1
Iterations
IterNodes
done5001
62514
5896
4344
3126
246
123
011

prune32.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 13.9b

localize53.0ms

Local error

Found 2 expressions with local error:

0.0b
(/ (- t x) (- a z))
14.0b
(fma (/ (- t x) (- a z)) (- y z) x)

rewrite63.0ms

Algorithm
rewrite-expression-head
Rules
38×add-sqr-sqrt *-un-lft-identity
25×times-frac
14×add-cube-cbrt
12×distribute-lft-out-- difference-of-squares
5×associate-/r* associate-/l*
4×add-exp-log add-cbrt-cube
2×pow1 expm1-log1p-u flip3-- associate-/r/ flip-- log1p-expm1-u associate-/l/ add-log-exp
1×cbrt-undiv frac-2neg div-sub div-exp clear-num fma-udef div-inv
Counts
2 → 64
Calls
2 calls:
54.0ms
(/ (- t x) (- a z))
4.0ms
(fma (/ (- t x) (- a z)) (- y z) x)

series333.0ms

Counts
2 → 6
Calls
2 calls:
116.0ms
(/ (- t x) (- a z))
217.0ms
(fma (/ (- t x) (- a z)) (- y z) x)

simplify3.2s

Counts
70 → 70
Iterations
IterNodes
done5014
32160
2670
1274
0118

prune772.0ms

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 9.0b

localize47.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ (- t x) (- a z))
3.9b
(+ x (* (- y z) (/ (- t x) (- a z))))
4.0b
(* (- y z) (/ (- t x) (- a z)))

rewrite191.0ms

Algorithm
rewrite-expression-head
Rules
79×add-sqr-sqrt
74×*-un-lft-identity
51×times-frac
31×associate-*r*
28×add-cube-cbrt
23×distribute-lft-out-- difference-of-squares
10×add-exp-log add-cbrt-cube
5×pow1 flip3-- associate-*l* associate-/r* flip-- associate-/l* add-log-exp
4×associate-/r/
3×expm1-log1p-u fma-def log1p-expm1-u
2×cbrt-undiv frac-times div-exp associate-*l/ prod-exp cbrt-unprod div-inv associate-/l/ unswap-sqr
1×+-commutative frac-2neg flip3-+ div-sub associate-*r/ pow-prod-down clear-num sum-log *-commutative flip-+
Counts
3 → 128
Calls
3 calls:
50.0ms
(/ (- t x) (- a z))
12.0ms
(+ x (* (- y z) (/ (- t x) (- a z))))
118.0ms
(* (- y z) (/ (- t x) (- a z)))

series738.0ms

Counts
3 → 9
Calls
3 calls:
135.0ms
(/ (- t x) (- a z))
334.0ms
(+ x (* (- y z) (/ (- t x) (- a z))))
268.0ms
(* (- y z) (/ (- t x) (- a z)))

simplify5.2s

Counts
137 → 137
Iterations
IterNodes
done5001
21823
1515
0189

prune2.1s

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 5.5b

localize64.0ms

Local error

Found 4 expressions with local error:

0.5b
(cbrt (- a z))
0.5b
(cbrt (- a z))
1.3b
(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z))))
8.5b
(+ x (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))))

rewrite607.0ms

Algorithm
rewrite-expression-head
Rules
76×add-sqr-sqrt
60×*-un-lft-identity
52×times-frac
46×associate-*r*
37×cbrt-prod
28×add-cube-cbrt
25×add-exp-log
18×cbrt-div add-cbrt-cube
17×associate-*l*
16×distribute-lft-out-- difference-of-squares
10×associate-/r/
9×flip3-- flip--
8×prod-exp cbrt-unprod
7×cbrt-undiv div-exp
6×pow1 add-log-exp unswap-sqr
5×frac-times
4×expm1-log1p-u log1p-expm1-u
3×fma-def associate-*r/ associate-*l/
2×pow1/3 div-inv
1×+-commutative flip3-+ pow-prod-down sum-log *-commutative flip-+
Counts
4 → 145
Calls
4 calls:
25.0ms
(cbrt (- a z))
9.0ms
(cbrt (- a z))
364.0ms
(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z))))
18.0ms
(+ x (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))))

series2.7s

Counts
4 → 12
Calls
4 calls:
782.0ms
(cbrt (- a z))
571.0ms
(cbrt (- a z))
934.0ms
(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z))))
383.0ms
(+ x (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))))

simplify10.8s

Counts
157 → 157
Iterations
IterNodes
done5000
22961
1761
0261

prune4.4s

Pruning

17 alts after pruning (16 fresh and 1 done)

Merged error: 5.5b

localize104.0ms

Local error

Found 4 expressions with local error:

0.5b
(cbrt (- y z))
0.5b
(cbrt (- y z))
0.6b
(* (/ (* (cbrt (- y z)) (cbrt (- y z))) (cbrt (- a z))) (* (/ (cbrt (- y z)) (cbrt (- a z))) (/ (- t x) (cbrt (- a z)))))
5.1b
(+ x (* (/ (* (cbrt (- y z)) (cbrt (- y z))) (cbrt (- a z))) (* (/ (cbrt (- y z)) (cbrt (- a z))) (/ (- t x) (cbrt (- a z))))))

rewrite446.0ms

Algorithm
rewrite-expression-head
Rules
73×add-exp-log
35×add-cbrt-cube
32×prod-exp cbrt-unprod
22×cbrt-undiv div-exp
16×add-sqr-sqrt *-un-lft-identity
15×cbrt-prod
14×associate-*l*
10×add-cube-cbrt
9×pow1
8×times-frac
6×cbrt-div add-log-exp
5×frac-times associate-*r/
4×expm1-log1p-u log1p-expm1-u
3×flip3-- fma-def pow-prod-down associate-*l/ flip-- distribute-lft-out-- difference-of-squares
2×pow1/3 associate-/r/
1×+-commutative flip3-+ associate-*r* sum-log *-commutative flip-+ div-inv
Counts
4 → 114
Calls
4 calls:
8.0ms
(cbrt (- y z))
6.0ms
(cbrt (- y z))
397.0ms
(* (/ (* (cbrt (- y z)) (cbrt (- y z))) (cbrt (- a z))) (* (/ (cbrt (- y z)) (cbrt (- a z))) (/ (- t x) (cbrt (- a z)))))
19.0ms
(+ x (* (/ (* (cbrt (- y z)) (cbrt (- y z))) (cbrt (- a z))) (* (/ (cbrt (- y z)) (cbrt (- a z))) (/ (- t x) (cbrt (- a z))))))

series2.7s

Counts
4 → 12
Calls
4 calls:
454.0ms
(cbrt (- y z))
340.0ms
(cbrt (- y z))
1.2s
(* (/ (* (cbrt (- y z)) (cbrt (- y z))) (cbrt (- a z))) (* (/ (cbrt (- y z)) (cbrt (- a z))) (/ (- t x) (cbrt (- a z)))))
726.0ms
(+ x (* (/ (* (cbrt (- y z)) (cbrt (- y z))) (cbrt (- a z))) (* (/ (cbrt (- y z)) (cbrt (- a z))) (/ (- t x) (cbrt (- a z))))))

simplify7.7s

Counts
126 → 126
Iterations
IterNodes
done5001
22177
1630
0231

prune1.9s

Pruning

17 alts after pruning (16 fresh and 1 done)

Merged error: 5.5b

regimes2.6s

Accuracy

5.7% (8.2b remaining)

Error of 12.1b against oracle of 3.9b and baseline of 12.6b

bsearch106.0ms

Steps
ItersRangePoint
6
1.295250367081412e+236
9.2033427507329e+236
1.8631297123296105e+236

simplify12.0ms

Iterations
IterNodes
done35
135
029

end0.0ms

sample3.7s

Algorithm
intervals
Results
2.0s7783×body80valid
223.0ms479×body640valid
132.0ms293×body1280valid
128.0ms418×body320valid
40.0ms256×body160valid
12.0ms15×body2560valid